Consider a list of m names, where the same name may appear more than once on the list. Let n(i), i = 1,... ,m, denote the number of times that the name in position i appears on the list, and let d denote the number of distinct names on the list.
(a) Express d in terms of the variables m, n(i),i = 1,..., m. Let U be a uniform (0, 1) random variable, and let X = [mU] + 1.
(b) What is the probability mass function of X?
(c) Argue that E[m/n(X)] = d.
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